Automatic Convexity Deduction for Efficient Function’s Range Boundingстатья
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Дата последнего поиска статьи во внешних источниках: 3 февраля 2022 г.
Аннотация:Reliable bounding of a function’s range is essential for deterministic global optimization,approximation, locating roots of nonlinear equations, and several other computational mathematicsareas. Despite years of extensive research in this direction, there is still room for improvement.The traditional and compelling approach to this problem is interval analysis. We show that accountingconvexity/concavity can significantly tighten the bounds computed by interval analysis. To makeour approach applicable to a broad range of functions, we also develop the techniques for handlingnondifferentiable composite functions. Traditional ways to ensure the convexity fail in such cases.Experimental evaluation showed the remarkable potential of the proposed methods